The second recipe of this chapter showed you how to compute the fundamental matrix of an image pair from a set of matches. In projective geometry, another very useful mathematical entity also exists. This one can be computed from multiview imagery and, as we will see, is a matrix with special properties.
Again, let's consider the projective relation between a 3D point and its image on a camera, which we introduced in the first recipe of this chapter. Basically, we learned that this equation relates a 3D point with its image using the intrinsic properties of the camera and the position of this camera (specified with a rotation and a translation component). If we now carefully examine this equation, we realize that there are two special situations of particular interest. The first situation is when two views of a scene are separated by a pure rotation. It can then be observed that the fourth column of the extrinsic matrix will be made up...